BUFFALO—New York Gov. Andrew Cuomo's campaign on Wednesday tried to move past Tuesday night's primary, when he scored a victory over a liberal challenger but one that came with an asterisk not easily removed.

At an raucous victory celebration here at Buffalo Niagara Convention Center, no fewer than 40 signs and banners proclaimed his name. Elected officials praised his "huge victory" and called him "the greatest governor the state of New York has ever had."